HELPEPEPEP PLEAS Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A E, B F, and C D. The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6.
G is the centroid of triangle ABC.

What is the length of AE?

units

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

0.02040816326

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